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Irreducible Representations of Braid Groups of corank two  [PDF]
Inna Sysoeva
Mathematics , 2000,
Abstract: This paper is the first part of a series of papers aimed at improving the classification by Formanek of the irreducible representations of Artin braid groups of small dimension. In this paper we classify all the irreducible complex representations $\rho$ of Artin braid group $B_n$ with the condition $rank (\rho (\sigma_i)-1)=2$ where $\sigma_i$ are the standard generators. For $n \geq 7$ they all belong to some one-parameter family of $n$-dimensional representations.
Most irreducible representations of the 3-string braid group  [PDF]
Lieven Le Bruyn
Mathematics , 2013,
Abstract: As the 3-string braid group B(3) and the modular group PSL(2,Z) are both of wild representation type one cannot expect a full classification of all their finite dimensional simple representations. Still, one can aim to describe 'most' irreducible representations by constructing for each d-dimensional irreducible component X of the variety iss(n,B(3)) classifying the isomorphism classes of semi-simple n-dimensional representations of B(3) an explicit minimal etale rational map A^d --> X having a Zariski dense image. Such rational dense parametrizations were obtained for all components when n < 12 in \cite{arXiv:1003.1610v1}. The aim of the present paper is to establish such parametrizations for all finite dimensions n.
Quantum Teichmuller theory and representations of the pure braid group  [PDF]
Francis Bonahon
Mathematics , 2008,
Abstract: We adapt some of the methods of quantum Teichm\"uller theory to construct a family of representations of the pure braid group of the sphere.
Some irreducible representations of the braid group B_n of dimension greater than n  [PDF]
Claudia Maria Egea,Esther Galina
Mathematics , 2008, DOI: 10.1142/10.1142/S0218216510007966
Abstract: For any n>3, we give a family of finite dimensional irreducible representations of the braid group B_n. Moreover, we give a subfamily parametrized by 0
$N$-Dimensional Representations of the Braid Groups $B_{N}$  [PDF]
Dian-Min Tong,Shan-De Yang,Zhong-Qi Ma
Physics , 1994,
Abstract: In this note, a new class of representations of the braid groups $B_{N}$ is constructed. It is proved that those representations contain three kinds of irreducible representations: the trivial (identity) one, the Burau one, and an $N$-dimensional one. The explicit form of the $N$-dimensional irreducible representation of the braid group $B_{N}$ is given here.
A note on certain finite-dimensional representations of the braid group  [PDF]
Valentin Vankov Iliev
Mathematics , 2010,
Abstract: In this paper the author finds explicitly all finite-dimensional irreducible representations of a series of finite permutation groups that are homomorphic images of Artin braid group.
On the irreducibility of linear representations of the pure braid group  [cached]
Mohammad N. Abdulrahim
Tamkang Journal of Mathematics , 2010, DOI: 10.5556/j.tkjm.41.2010.283-292
Abstract: Following up on our result in [1], we find a milder sufficient condition for the tensor product of specializations of the reduced Gassner representation of the pure braid group to be irreducible. We prove that $G_n(x_1, ldots, x_n) otimes G_n(y_1, ldots, y_n) : P_n o GL(mathbb{C}^{n-1} otimes mathbb{C}^{n-1})$ is irreducible if $x_i eq pm y_i $ and $x_j eq pm {{y_j}^{-1}} $ for some $i$ and $j$.
Higher generation for pure braid groups  [PDF]
Matthew C. B. Zaremsky
Mathematics , 2012,
Abstract: We exhibit some families of subgroups of the pure braid group that are highly generating, in the sense of Abels and Holz. In one class of examples, the relevant geometric object is a complex termed the restricted arc complex of a surface. Another arises by considering "dangling braiges," introduced by Bux, Fluch, Schwandt, Witzel and the author.
On the Linearized Artin Braid Representation  [PDF]
F. Constantinescu,F. Toppan
Physics , 1992,
Abstract: We linearize the Artin representation of the braid group given by (right) automorphisms of a free group providing a linear faithful representation of the braid group. This result is generalized to obtain linear representations for the coloured braid groupoid and pure braid group too. Applications to some areas of two-dimensional physics are discussed.
High-dimensional representations of the 3-component loop braid group  [PDF]
Lieven Le Bruyn
Mathematics , 2015,
Abstract: In a recent paper here arXiv:1508.0005 it is shown that irreducible representations of the three string braid group $B_3$ of dimensions $\leq 5$ extend to representations of the 3-component loop braid group $LB_3$. Further, an explicit $6$-dimensional irreducible $B_3$-representation is given that does not extend. In this note we give a necessary and sufficient condition on the components of irreducible $B_3$-representations, in arbitrary dimensions, such that sufficiently general representations in that component do extend to $LB_3$.
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